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\begin{equation}
W=\left| \begin{array}{cc} y_1 &amp; y_2 \\ y_1^{\prime} &amp; y_2^{\prime}     \end{array} \right|=
\left| \begin{array}{cc} e^{r_1 x} &amp; e^{r_2 x} \\ r_1 e^{r_1 x} &amp;r_2 e^{r_2 x}     \end{array} \right|
=r_2 e^{(r_1+r_2)x}-r_1 e^{(r_1+r_2)x} =(r_2-r_1) e^{(r_1+r_2)x} \neq 0.\tag{3.2.3}
\end{equation}
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